...theories and unreal situations. Are you going to add lead and swing faster?...only if you were swingly slowly in the first place and are capable of swinging faster.

Physics from a lay person, not someone who's actually studied physics. You know there's a problem with their "physics" explanation just because it contradicts with what you find experimentally.

F = ma (force = mass x acceleration)

That's not complicated physics. It's taught in any high school physics class. If you increase the mass of the racquet, and the a (acceleration) remains constant (that is, if you are capable of accelerating the racquet just as much after adding lead as you were before adding lead), then the F will be greater.

You said "you know there's a problem with their 'physics' explanation just because it contradicts with what you find experimentally."

If you are finding experimentally that after increasing the mass of the racquet, you are getting less power, then you are either not swinging as quickly as you were before, or your perception is off (not to mention is pretty high degree of error in one's ability to perceive a general increase or decrease in power, since they are so many variables at play in any given shot).